The universe we know is fundamentally probabilistic, so by extension everything including stars, planets and computers are inherently non-deterministic. But confining our discussion outside of quantum effects and absolute determinism, we do not have a reason to believe that the mind should be anything but deterministic, scientifically at least.

We understand the building blocks of the brain pretty well. We know the structure and composition of neurons, we know how they are connected, what chemicals flow through them and how all these chemicals interact, and how that interaction translates to signal propagation. In fact, the neural networks we use in computing are loosely modelled on biological neurons. Both models are essentially comprised of interconnected units where each unit has weights to convert its incoming signals to outgoing signals. The predominant difference is in how these units adjust their weights, where computational models use back propagation and gradient descent, biological models use timing information from voltage changes.

But just because we understand the science of something perfectly well, doesn't mean we can precisely predict how something will work. Biological networks are very, very complex systems comprising of billions of neurons with trillions of connections acting on input that can vary in immeasurable number of ways. It's like predicting earthquakes. Even though we understand the science behind plate tectonics, to precisely predict an earthquake we need to map the properties of every inch of continental plates which is an impossible task. But doesn't mean we can't use the same scientific building blocks to build simulations of earthquakes which behave like any real earthquake would behave. If it looks like a duck, quacks like a duck, then what is a duck?

Seems to me you are a bit overconfident that "we" (who is "we"?) understand how the brain works. F.ex. how does a neuron actively stretching a tentacle trying to reach other neurons work in your model? Genuine question, I am not looking to make fun of you, it's just that your confidence seems a bit much.